Question

What are the roots of the equation x² −4x+5?

A) 1+i and 1−i
B) 2+i and 2−i
C) 3+i and 3−i
D) 4+i and 4−i

Answer 1

The roots of the equation x² - 4x + 5 are 2 + i and 2 - i.

The Correct option is; B) 2 + i and 2 - i.

Step-by-step explanation:

The roots of the equation x² - 4x + 5 can be found using the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the roots can be calculated using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = -4, and c = 5. Substituting these values into the formula:

x = (-(-4) ± √((-4)² - 4(1)(5))) / (2(1))

Simplifying further:

x = (4 ± √(16 - 20)) / 2

x = (4 ± √(-4)) / 2

x = (4 ± 2i) / 2

x = 2 ± i

Therefore, the roots of the equation are 2 + i and 2 - i, which corresponds to option B) 2 + i and 2 - i.